3 4 Properties of Logarithmic Functions Copyright 2011

  • Slides: 17
Download presentation
3. 4 Properties of Logarithmic Functions Copyright © 2011 Pearson, Inc.

3. 4 Properties of Logarithmic Functions Copyright © 2011 Pearson, Inc.

What you’ll learn about n n Properties of Logarithms Change of Base Graphs of

What you’ll learn about n n Properties of Logarithms Change of Base Graphs of Logarithmic Functions with Base b Re-expressing Data … and why The applications of logarithms are based on their many special properties, so learn them well. Copyright © 2011 Pearson, Inc. Slide 3. 4 - 2

Properties of Logarithms Copyright © 2011 Pearson, Inc. Slide 3. 4 - 3

Properties of Logarithms Copyright © 2011 Pearson, Inc. Slide 3. 4 - 3

Example Proving the Product Rule for Logarithms Copyright © 2011 Pearson, Inc. Slide 3.

Example Proving the Product Rule for Logarithms Copyright © 2011 Pearson, Inc. Slide 3. 4 - 4

Example Proving the Product Rule for Logarithms Copyright © 2011 Pearson, Inc. Slide 3.

Example Proving the Product Rule for Logarithms Copyright © 2011 Pearson, Inc. Slide 3. 4 - 5

Example Expanding the Logarithm of a Product Copyright © 2011 Pearson, Inc. Slide 3.

Example Expanding the Logarithm of a Product Copyright © 2011 Pearson, Inc. Slide 3. 4 - 6

Example Expanding the Logarithm of a Product Copyright © 2011 Pearson, Inc. Slide 3.

Example Expanding the Logarithm of a Product Copyright © 2011 Pearson, Inc. Slide 3. 4 - 7

Example Condensing a Logarithmic Expression Copyright © 2011 Pearson, Inc. Slide 3. 4 -

Example Condensing a Logarithmic Expression Copyright © 2011 Pearson, Inc. Slide 3. 4 - 8

Example Condensing a Logarithmic Expression Copyright © 2011 Pearson, Inc. Slide 3. 4 -

Example Condensing a Logarithmic Expression Copyright © 2011 Pearson, Inc. Slide 3. 4 - 9

Change-of-Base Formula for Logarithms Copyright © 2011 Pearson, Inc. Slide 3. 4 - 10

Change-of-Base Formula for Logarithms Copyright © 2011 Pearson, Inc. Slide 3. 4 - 10

Example Evaluating Logarithms by Changing the Base Copyright © 2011 Pearson, Inc. Slide 3.

Example Evaluating Logarithms by Changing the Base Copyright © 2011 Pearson, Inc. Slide 3. 4 - 11

Example Evaluating Logarithms by Changing the Base Copyright © 2011 Pearson, Inc. Slide 3.

Example Evaluating Logarithms by Changing the Base Copyright © 2011 Pearson, Inc. Slide 3. 4 - 12

Example Transforming Logarithmic Graphs log x Copyright © 2011 Pearson, Inc. Slide 3. 4

Example Transforming Logarithmic Graphs log x Copyright © 2011 Pearson, Inc. Slide 3. 4 - 13

Example Transforming Logarithmic Graphs Copyright © 2011 Pearson, Inc. Slide 3. 4 - 14

Example Transforming Logarithmic Graphs Copyright © 2011 Pearson, Inc. Slide 3. 4 - 14

Example Transforming Logarithmic Graphs log x Since log x= Copyright © 2011 Pearson, Inc.

Example Transforming Logarithmic Graphs log x Since log x= Copyright © 2011 Pearson, Inc. Slide 3. 4 - 15

Quick Review Copyright © 2011 Pearson, Inc. Slide 3. 4 - 16

Quick Review Copyright © 2011 Pearson, Inc. Slide 3. 4 - 16

Quick Review Solutions Copyright © 2011 Pearson, Inc. Slide 3. 4 - 17

Quick Review Solutions Copyright © 2011 Pearson, Inc. Slide 3. 4 - 17

4 3 Logarithmic Functions Logarithmic Equations Logarithmic Functions4 3 Logarithmic Functions Logarithmic Equations Logarithmic Functions
Exponential and Logarithmic Functions 5 Exponential Functions LogarithmicExponential and Logarithmic Functions 5 Exponential Functions Logarithmic
Exponential and Logarithmic Functions 5 Exponential Functions LogarithmicExponential and Logarithmic Functions 5 Exponential Functions Logarithmic
Logarithmic functions LO Sketch logarithmic functions The graphLogarithmic functions LO Sketch logarithmic functions The graph
Unit VII Logarithmic Functions Section VIIA Logarithmic FunctionsUnit VII Logarithmic Functions Section VIIA Logarithmic Functions
3 4 Properties of Logarithmic Functions Copyright 20113 4 Properties of Logarithmic Functions Copyright 2011
Logarithmic Functions The logarithmic function to the baseLogarithmic Functions The logarithmic function to the base
Definition LOGARITHMIC FUNCTIONS of the logarithmic function TranslationDefinition LOGARITHMIC FUNCTIONS of the logarithmic function Translation
5 Exponential and Logarithmic Functions EXPONENTIAL AND LOGARITHMIC5 Exponential and Logarithmic Functions EXPONENTIAL AND LOGARITHMIC
5 Exponential and Logarithmic Functions Exponential and Logarithmic5 Exponential and Logarithmic Functions Exponential and Logarithmic
Logarithmic Functions The logarithmic function to the baseLogarithmic Functions The logarithmic function to the base
Logarithmic Functions PRECALCULUS UNIT 3 EXPONENTIAL AND LOGARITHMICLogarithmic Functions PRECALCULUS UNIT 3 EXPONENTIAL AND LOGARITHMIC
Logarithmic Functions The logarithmic function to the baseLogarithmic Functions The logarithmic function to the base
8 2 Transformations of Logarithmic Functions Exponent Logarithmic8 2 Transformations of Logarithmic Functions Exponent Logarithmic
Logarithmic Functions 3 2 The logarithmic function toLogarithmic Functions 3 2 The logarithmic function to
The Exponential Logarithmic Functions Exponential Graph Logarithmic GraphThe Exponential Logarithmic Functions Exponential Graph Logarithmic Graph